Dynamics of a Fokker–Planck type diffusion epidemic model with general incidence and relapse

Abstract

In this paper, a spatially heterogeneous SIRI epidemic model with general morbidity is studied, which conforms to the Fokker–Planck type diffusion law. The basic reproduction number R0 of the model is introduced, and the threshold dynamics based on R0 is discussed. In particular, with the help of elliptic eigenvalue theory, we determine the asymptotic profiles of the endemic equilibrium when the diffusion rate of susceptible individuals approaches zero or infinity.